Naslov
2-categorical descent, monoidal actions and Hopf algebras

Autori
Škoda, Zoran

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
New techniques in Hopf algebras and graded ring theory

Mjesto i datum
Bruxelles, Belgija, 19.09.2006. - 23.09.2006

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
descent theory; Hopf modules; monoidal categories; distributive laws; equivariant objects; 2-categories

Sažetak
In Tannakian philosophy, roughly speaking, Hopf algebras are interchangeable with their categories of modules. Similarly when globalizing actions of Hopf algebras to nonaffine situations, describing the situation in terms of categorical actions is unavoidable. I will describe several examples where this point of view is very fruitful, leading to appropriate versions of actions on noncommutative projective varieties, including quantum flag variaties, corresponding equivariant sheaves, giving a framework for natural appearance of distributive laws like entwining structures and more general ones. This is also the framework in which some related notions, like lax versions of descent may be treated. Duskin has considered 2-categorical descent in 1980-s. Ordinary descent data in Galois descent along torsors correspond to equivariant sheaves. I developed a 2-categorical analogue of equivariant objects with aim to develop a 2-Galois theory yielding an 2-equivalence between the 2-category of equivariant sheaves on torsor of a categorical group and the 2-category of ordinary sheaves on the base.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA